Instability of bound states of a nonlinear Schrödinger equation with a Dirac potential

We study analytically and numerically the stability of the standing waves for a nonlinear Schrödinger equation with a point defect and a power type nonlinearity. A major difficulty is to compute the number of negative eigenvalues of the linearized operator around the standing waves. This is overcome by a perturbation method and continuation arguments. Among others, in the case of a repulsive defect, we show that the standing-wave solution is stable in and unstable in under subcritical nonlinearity. Further we investigate the nature of instability: under critical or supercritical nonlinear interaction, we prove the instability by blowup in the repulsive case by showing a virial theorem and using a minimization method involving two constraints. In the subcritical radial case, unstable bound states cannot collapse, but rather narrow down until they reach the stable regime (a finite-width instability). In the nonradial repulsive case, all bound states are unstable, and the instability is manifested by a lateral drift away from the defect, sometimes in combination with a finite-width instability or a blowup instability.     

Zwei Sätze über Differential-und Differenzenquotient von analytischen Funktionen

Ohne Zusammenfassung     

Zur Theorie verallgemeinerter torsaler Strahlflächen

In this paper we will investigate (k+1)-dimensional generalized ruled surfaces generated by a one-parameter family ofk-dimensional linear subspaces of then-dimensional Euclidean spaceE _n . Some results which are well-known for developable surfaces are proved for generalized ruled surfaces: Generalized developable surfaces are locally either cyclinders, cones or tangent surfaces. Each regular surface on a generalized ruled surface is locally Euclidean if and only if is developable. Each locally Euclidean hypersurface is a generalized developable hypersurface. Furthermore, the hypersurfaces with vanishing Gaussian curvature and the locally Euclidean hypersurfaces on generalized rule hypersurfaces will be characterized.     

In-beam γ-spectroscopy with relativistic radioactive ion beams

This work demonstrates the feasibility of in-beam %-spectroscopy employing radioactive ion beam species at relativistic energies of E = 210 ~ 280 A · MeV. Neutron-rich nuclei below ⁴⁸Ca with neutron number between the two magic numbers 20 and 28 have been investigated. Using a Pb target, single step inelastic excitation originating mainly from Coulomb interaction takes place populating preferentially low-lying low-spin states and enabling the extraction of B(E2) values. On a C target, nucleon removal reactions are dominating and medium-spin states are populated thus offering spectroscopic information in neighboring nuclei. Cross sections of inelastic excitation are determined and compared to coupled-channels calculations. Two new states of the very neutron-rich nucleus ⁴⁴Ar at 1.78(8) MeV and 2.61(16) MeV are deduced from %-transitions.     

Reaction and fission cross-sections of 750 A·MeV238U ions on Pb,Cu and Al-targets

Charge-loss and fission cross-sections of²³⁸U at 750 A·MeV were measured on Al, Cu and Pb targets. The charge-loss rate was obtained by the attenuation method. Fission was selected by detecting the pair of highly ionizing fragments. Since the neutron-loss cross sections were measured in a parallel experiment for the same projectiles, all cross sections contributing to²³⁸U collisions on nuclei are available now as function of the target mass number and can be compared with current models.     

Einige Bemerkungen über Quadriken in affinen Räumen

Zusammenfassung. Es wird bewiesen, da? die Gleichung einer nicht nullteiligen Quadrik eines affinen Raums bis auf einen von Null verschiedenen Faktor eindeutig bestimmt ist. Ferner wird gezeigt, da? es keine wesentliche Einschr?nkung bedeutet, sich bei der Untersuchung der Quadriken auf nicht nullteilige Quadriken zu beschr?nken, falls der zugrundeliegende K?rper mehr als drei Elemente enth?lt, da dann die nullteiligen Quadriken (als Punktmengen) affine Unterr?ume sind. Eingegangen am 20.4.1994, angenommen am 9.1.1995     

Aufbau von Mittelwerten mehrerer Argumente. II. (Analytische Mittelwerte.)

Ohne Zusammenfassung     

Unifying model for several classes of two-dimensional phase transition

A relatively simple and physically transparent model based on quantum percolation and dephasing is employed to construct a global phase diagram which encodes and unifies the critical physics of the quantum Hall, "two-dimensional metal-insulator," classical percolation and, to some extent, superconductor-insulator transitions. Using real-space renormalization group techniques, crossover functions between critical points are calculated. The critical behavior around each fixed point is analyzed and some experimentally relevant puzzles are addressed.